# summary.l1ce: Summary Method for "l1ce" Objects (Regression with L1... In lasso2: L1 Constrained Estimation aka `lasso'

## Description

Returns a summary list for a regression model with an L1 constraint on the parameters. A null value will be returned if printing is invoked.

## Usage

 ```1 2 3 4 5 6``` ```## S3 method for class 'l1ce' summary(object, correlation = TRUE, type = c("OPT", "Tibshirani"), gen.inverse.diag = 0, sigma = NULL, ...) ## S3 method for class 'summary.l1ce' print(x, digits = max(3, getOption("digits") - 3), ...) ```

## Arguments

 `object` fitted model of class `"l1ce"`. `correlation` logical indicating if the correlation matrix for the coefficients should be included in the summary. `type` character string specifying whether to use the covariance formula of Osborne, Presnell and Turlach or the formula of Tibshirani. `gen.inverse.diag` if Tibshirani's formula for the covariance matrix is used, this value is used for the diagonal elements of the generalised inverse that appears in the formula that corresponds to parameters estimated to be zero. The default is 0, i.e. use the Moore-Penrose inverse. Tibshirani's code uses gen.inverse.diag=1e11. `sigma` the residual standard error estimate. If not provided, then it is estimated by the deviance of the model divided by the error degrees of freedom. `x` an R object of class `summary.l1ce`. `digits` number of significant digits to use. `...` further potential arguments passed to methods.

## Details

This function is a method for the generic function `summary()` for class `"l1ce"`. It can be invoked by calling `summary(x)` for an object `x` of the appropriate class, or directly by calling `summary.l1ce(x)` regardless of the class of the object.

## Value

an object of class `summary.l1ce` (for which there's a `print` method). It is basically a list with the following components:

 `correlation` the computed correlation coefficient matrix for the coefficients in the model. `cov.unscaled` the unscaled covariance matrix; i.e, a matrix such that multiplying it by an estimate of the error variance produces an estimated covariance matrix for the coefficients. `df` the number of degrees of freedom for the model and for residuals. `coefficients` a matrix with three columns, containing the coefficients, their standard errors and the corresponding t statistic. `residuals` the model residuals. These are the weighted residuals if weights were given in the model. `sigma` the residual standard error estimate. `terms` the terms object used in fitting this model. `call` the call object used in fitting this model. `bound` the bound used in fitting this model. `relative.bound` the relative bound used in fitting this model (may not be present). `Lagrangian` the Lagrangian of the model.

`l1ce`, `l1ce.object`, `summary`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```data(Prostate) summary(l1ce(lpsa ~ .,Prostate)) # Produces the following output: ## Not run: Call: l1ce(formula = lpsa ~ ., data = Prostate) Residuals: Min 1Q Median 3Q Max -1.636 -0.4119 0.076 0.452 1.83 Coefficients: Value Std. Error Z score Pr(>|Z|) (Intercept) 0.7285 1.3898 0.5242 0.6002 lcavol 0.4937 0.0919 5.3711 0.0000 lweight 0.2682 0.1774 1.5115 0.1307 age 0.0000 0.0111 0.0000 1.0000 lbph 0.0093 0.0587 0.1581 0.8744 svi 0.4551 0.2525 1.8023 0.0715 lcp 0.0000 0.0947 0.0000 1.0000 gleason 0.0000 0.1685 0.0000 1.0000 pgg45 0.0002 0.0046 0.0391 0.9688 Residual standard error: 0.7595 on 88.36 degrees of freedom The relative L1 bound was : 0.5 The absolute L1 bound was : 0.9219925 The Lagrangian for the bound is: 13.05806 Correlation of Coefficients: (Intercept) lcavol lweight age lbph svi lcp gleason lcavol 0.1988 lweight -0.4815 -0.2071 age -0.3938 -0.0603 -0.0974 lbph 0.3629 -0.0201 -0.5165 -0.1303 svi -0.0624 -0.2273 -0.1442 0.0635 0.0648 lcp 0.0457 -0.4153 0.0598 0.0665 0.0632 -0.3779 gleason -0.7666 -0.2009 0.1163 -0.0774 -0.0617 0.1084 -0.0243 pgg45 0.4988 0.0956 -0.0380 -0.0630 -0.1111 -0.1921 -0.2935 -0.6526 ## End(Not run) ```